Problem: Solve for $j$. $-\dfrac13=\dfrac j{4}-\dfrac{10}3 $
Solution: Let's add and then multiply to get $j$ by itself. $\begin{aligned}-\dfrac13&=\dfrac j{4}-\dfrac{10}3 \\ \\ -\dfrac13{+\dfrac{10}3} &=\dfrac j{4}-\dfrac{10}3 {+\dfrac{10}3}~~~~~~~~{\text{add }\dfrac{10}3} \text{ to each side}\\ \\ -\dfrac13{+\dfrac{10}3}&=\dfrac j{4}-\cancel{ \dfrac{10}3} {{+}\cancel{{\dfrac{10}3}}}\\ \\ -\dfrac13{+\dfrac{10}3}&=\dfrac j{4} \\\\ \dfrac93&=\dfrac j{4} \end{aligned}$ $\begin{aligned}3&= \dfrac j{4} \\ \\ {3}\cdot{{4}} &= \dfrac j{4}\cdot{{4}} ~~~~~~~\text{multiply each side by } {4} \text{ to get } j \text{ by itself }\\ \\ {3}\cdot{{4}} &= \dfrac j{\cancel{4}}\cdot{\cancel{{4}}} \\ \\ {3}\cdot{{4}} &= j \end{aligned}$ The answer: $j={12}$ Let's check to make sure. $\begin{aligned} -\dfrac13&=\dfrac j{4}-\dfrac{10}3\\\\ -\dfrac13&\stackrel{?}{=} \dfrac{{12}}{4}-\dfrac{10}3 \\\\ -\dfrac13&\stackrel{?}{=} 3-\dfrac{10}3 \\\\ -\dfrac13&\stackrel{?}{=} \dfrac93-\dfrac{10}3 \\\\ -\dfrac13&=-\dfrac13 ~~~~~~~~~~\text{Yes!} \end{aligned}$